Four months before a best-selling Alzheimer’s drug was set to lose its patent protection, its makers received approval for a higher dosage that extended their exclusive right to sell the drug. But the higher dosage caused potentially dangerous side effects and worked only slightly better than the existing drugs, according to an article published Thursday in the British Medical Journal. The drug, Aricept 23, was approved in July 2010 against the advice of reviewers at the Food and Drug Administration.